Lesson video

Hi, everyone.

My name is Ms. Jeremy.

Thank you for joining me for a maths lesson today.

Today, our focus is on investigating Roman numerals up to 1,000.

So get yourself sorted with a nice, quiet space, free from distractions and press play when you're ready to begin your lesson.

Okay, let's start by looking at your lesson agenda for today.

So today's warm up is going to be all about Roman numerals to 100, we'll be recapping those.

We'll then look at Roman numerals up to 1,000 and how to represent these.

And we'll then finish off with looking at some Roman numeral sequences before your independent task and quiz at the end of the lesson.

In today's lesson, you will need a pencil and some paper and a nice, quiet space.

So pause the video now to get your resources sorted, and once you're ready, press play to begin the lesson.

So let's start with our warm up.

The question asks, can you match the Roman numerals and Arabic numerals on the screen below? So on the left-hand side there, on the pink side, you can see a series of Roman numerals.

And on the right-hand side, on the blue, you can see a series of Arabic numerals.

Can you match them up? I'm going to give you 10 seconds to see whether you can match both sides.

Okay, how did you get on? And let's have a look together.

So let's have a look, first of all, at the first pink Roman numeral.

We can see there that we've got the number LVII.

So let's dissect this a little bit.

So we know the L stands for 50 and then VII stands for a 5, plus a 1, plus a 1, which is a 7, so that is equal to 57.

That's going to match up to our second number, 57.

Let's have a look at the next one.

Well, we've got an X and an L, first of all, and we know that if the X comes before the L, if a smaller Roman numeral is placed before a larger Roman numeral, we're subtracting it.

So we're going to do 50 minus 10.

That means that XL is equal to 40.

And then VIII is 8, because it's a 5 plus a 1, plus a 1, plus a 1.

So that is equal to 48, which is our first Roman numeral up on the screen there.

And the last one, we've got an LXX, first of all.

So let's have a look at that.

And LXX, we know L means 50, and we know XX means 20, so we're adding 50 plus 20, which is equal to 70.

And II means 2, so that is equal to 72.

We've matched up those Roman numerals.

So moving on and for the rest of the lesson, we'll be looking at Roman numerals up to 1,000.

In order for us to be able to represent the Roman numerals to 1,000, we're going to need to follow a set of rules, but we're also going to need to know a few base symbols.

Some of these you might have already seen when learning about Roman numerals up to 100.

Here they are on the screen.

So we know that an I stands for 1, V is five, X is 10, L is 50, and C is 100.

The new Roman numeral symbols that we need to know for today are the ones that are in green on your screen now.

We need to remember that D is equal to 500 and M is equal to 1,000.

Using all of that information and some of the key rules that I'm going to explain to you now, we can represent any number using Roman numerals up to 1,000.

So the first one of those key rules is that a Roman numeral symbol can not be used more than three times in a row in any one number.

So if you're trying to represent a particular number and you find that you need to use a symbol, a Roman numeral letter more than three times, you need to think of another way of representing that number.

I'll give you an example.

If I wanted to represent the number 40 using Roman numerals, I wouldn't be allowed to use four of the Xs in a row together.

I need to find another way to represent that symbol.

The other way to represent that number is to use the concept of 50 minus 10, and that introduces my other rule.

The other rule states that if you place a smaller valued Roman numeral symbol in front of a larger valued Roman numeral symbol, just like I've done there with the XL, then what that means is you are subtracting it from that larger.

So I know that the X means 10, the L means 50, and in this case, we're referring to 50 minus 10.

I like to think of it as the 10 before 50, which is of course, equal to 40.

Similarly, if you place a smaller Roman numeral symbol, after a larger Roman numeral symbol, like this, then you add it on.

So in this case, we know that our means 50 and X means 10.

We are adding on 50 plus 10, which is equal to 60.

So you can see that there are three key rules that we've already learned about.

Not using a symbol more than three times in a row, also making sure that we're placing symbols ahead of each other if we want to subtract, and after another symbol if we want to add.

Those three rules are crucial to representing Roman numerals all the way up to 1,000, and we will be using those today in the lesson.

So let's get started with looking at how we can use all of this information to represent the following numbers.

So I've got my little code, my little key here, to show me what the different Roman numerals represent and what they stand for.

And I'm going to show you how I would use those Roman numerals to represent the following new numbers on the left-hand side here.

The first thing I need to do is use a partitioning strategy to break up each of my numbers into their components.

So I'm going to start with 154.

What I know that I'm going to need to represent 100, I'm going to need to represent 50, and I'm going to need to represent 4.

And in order to do that, I'm going to start with my 100.

I can see straight away that I can use this symbol here.

I don't need to adapt it because C means 100.

Now I'm going to represent 50.

I'm going to use this symbol here, because that means 50.

And in order to represent 4 I don't have a number on there that directly represents 4, but I can use that rule where I place the I before the V because I know a V means 5 and the I going before it suggests that I'm subtracting 1 from 5, which would give me 4.

So that number means 154.

Let's have a go to the next one, 562.

So again, I need to partition out these numbers so I know what the components are.

I've got 500, I've got 60, I've got 2.

So once again, I've got a 500 symbol, which is the D.

I can use that straight away to represent 500.

Now, in order to represent 60, I'm going to use that rule where we place the 50 first, followed by the X, which means 10, and that represents 60.

And then to show 2, I'm going to use two of my Is.

DLXII, that represents 562.

The next one, 489.

So here, I'm breaking up into 400, 80, and 9.

So to represent 400, I'm not allowed to write CCCC because I'm not allowed to use the symbol more than three times in a row.

So instead, what I'm going to have to do is use my knowledge of what 500 is, which is D.

And if I write the D and I place a C before the D, that means 500 minus 100, 'cause C means 100.

So that means 400 there.

Then I've got to create 80, so I'm going to use my L, and then that means 50, then 60 for another X, 70, 80.

I'm going to probably have to move over to some more space outside the box.

And I still got to create 9.

I am going to create 9 using my knowledge that I before the X means 9, because that's 10 minus 1.

So that's a really long symbol that you can see that we've needed to use for creating 489.

923, let's have a look at this one together.

So first of all, we need to partition 923.

What are the different component parts of 923? I'm going to give you five seconds.

Okay, so hopefully you can see it is 900, then we've got to make 20, then we've got to make 3.

So to make 900, first of all, I need to think of a way to do this that's not going to involve me using a symbol more than three times in a row.

I'm going to have to use my knowledge of 1,000.

I know that M means 1,000, and I want to represent the 100 before 1,000.

I want to do 1,000 minus 100.

How would I represent that with a symbol on my Roman numerals? Three seconds.

So what I'm going to have to do is to put a C before the M because what that means is the M stands for 1,000, and because I placed the C just before it, I'm subtracting it, so that's 1,000 minus 100, and that represents 900.

Then I've got to represent 20, which I'm going to use my two Xs for.

And representing 3 with my three Is there.

CMXXIII, that's representative of 923.

So it's your turn to have a quick go.

Have a look at these four numbers on your screen.

Can you use the same strategies that we've been practising , using those same three rules that we've discussed to represent these four numbers using Roman numerals? Pause the video to complete your task and resume it once you're finished.

How did you get on? As you can see on the screen there, I've got the answers written down for you.

So pause the video now, just to mark the questions that you've completed and just check any areas that you've made and correct using the key that you've got on the side there.

Resume the lesson once you finished marking your learning.

So let's move on with our learning.

Now that we've learnt how to represent different Roman numerals, let's use that knowledge to solve some sequences involving Roman numerals.

So as you can see on the screen there, we've got two Roman numeral patterns, and they're either increasing or decreasing by the same amount.

What we're going to need to do is identify what each of those Roman numerals represent, write them down using our Arabic numeral system, and then use that information to work out what the following terms in the sequence will be writing these down using Roman numerals.

So let's look at the first one together.

I can see it's going up in by.

The first term is C, then CC, then CCC.

I'm going to give you five seconds to work out what those three numbers are representing.

Okay, so as you've seen, we're going up, our first number is 100, the second number is 200, third number is 300.

So nice, simple pattern.

And as you can probably imagine, we're going to be going up by hundreds each time.

So the next number will be 400 and the last number will be 500.

So my job now is to fill in those terms using Roman numerals.

I'm actually going to do 500 first of all.

I'm going to fill in the 500, because I know the 500 is represented by a D using the Roman numeral system.

Now I've got to work out how to represent 400.

I've got a couple of options for you.

I'd like you to work out which one is correct.

I can either represent 400 like this, CCCC.

I could represent it like this, DC.

Or I could represent it like this, CD.

Which of those is the correct to represent 400 and why? I'm going to give you five seconds to work that out.

Okay, have you chosen one? So let's go through them.

Well, the first one is incorrect because I cannot represent a symbol more than three times in a row using Roman numerals.

So even though C does mean 100, and 4 of them would technically represent 400, I'm not allowed to do that using the Roman numeral system, I have to find another way of representing without using the same Roman numeral more than three times.

The second one would represent, well, D means 500 and C means 100, but because the C has come after the D, I'd be adding it on.

That would show me 600.

That one's wrong.

The last one is the correct one, and the reason is that the C has come before the D.

Whenever you place a smaller Roman numeral before another Roman numeral, you're subtracting it, and so that would represent 400.

CD, I'll fill that in for you there.

Let's have a look at the second one now.

I'm going to give you 10 seconds to work out what each of the numbers in this sequence are.

Okay, so how did you get on? Let's have a look.

So let's look at the first one.

Well, I know that C means 100 and X is 10.

So CXX must be 120.

We've then got CC, that's 200, and then XL, so an X before an L, that means I'm taking away a 10 from a 50, 'cause L means 50, so that must be 240.

And then the last one is CCC, which means 300.

L which is 50, but then adding on an X, which is 10, so overall, LX means 60.

So I've got 120, 240, 360.

What is my sequence increasing by, and what is the next term in my sequence going to be? Five seconds.

So you might have spotted that each time we're increasing by 120, and we're adding on 120 each time.

So in order to find out the last term, I'm going to have to add 120.

360 plus 120 is equal to 480.

So how am I going to represent 400 and then 80? Five seconds to work it out.

Well, we've already discussed how to represent 400, because we did that in the first sequence.

That was using CD.

And then to represent 80, I need to use my 50, which is my L.

And then 60, 70, 80, I'm adding three 10s represented by Xs.

So CDLXXX, that's my final term in the sequence.

That really should be up there.

And the number should be below, the Arabic numerals should be below, but there we've represented both forms of 480.

So now it's your turn to have a go.

There are two sequences on the board.

Can you complete them using Roman numerals? Pause the video now to complete your task and resume once you're finished.

How did you get on? Let's have a look together and see how you did.

So the first sequence, the first thing that we're going to do is to identify what these different Roman numerals are representing in our sequences.

The first number is CCL.

I know C means 100 and L means 50.

So the first one must be CC, which is 250.

The next one is just a D, which means 500.

And I've got to work out the next number in my sequence.

Well, it looks like I'm going up in 250s each time.

So the next one will be 750, and the last one will be 1,000.

I know straight away that I can fill in the 1,000.

That is M, so I'll leave that one be, that's absolutely fine.

Now let's work out how to represent 750.

So, first of all, I want to represent 700.

I'm going to use my 500, which is D, plus 200 which is a CC, and then a 50 which is L, DCCL.

Okay, the next one.

Let's have a look.

DL, so I know that D means 500 and L means 50, so that must be 550.

Then D means 500.

And then here, I've got CD, which is equivalent to 400, and L means 50.

So looking at this, I can see I'm going down by 50 each time I'm decreasing.

So the next number I want to represent is 400, and then I want to represent 350, if I'm following the same pattern.

So to represent 400, we looked at this last time, we would do a C and a D because then we are subtracting the 100 from the 500.

And to represent 350, we can use CCC.

We're allowed to use a C more than.

We can use it three times in a row.

And then the 50 is represented using our L, just like that.

How did you get on? Give yourself a tick if you've got those one correct.

So just to finish off for the end of the lesson today, you've got a couple of tasks to complete for your independent task.

What I'd like you to do, first of all, is to look at question number one, you're going to write those numbers using Roman numerals.

For question two, you're going to do exactly the opposite.

You're going to look at those Roman numerals and write the numbers that correspond to those Roman numerals.

And then you've got two sequences to complete.

Pause the video to complete your task and then resume it once you're finished.

So let's have some look at some answers together.

What I'd like you to do is pause the video now to mark the questions that you completed.

How did you get on? How many did you get correct? Have a look at any that you've got incorrect and see if you can work out why.

We're at the end of the lesson now.

If you'd like to, please ask your parent or carer to share your work on Twitter tagging @OakNational and #LearnwithOak.

Anything left to do is to complete your quiz.

Thank you so much for joining me today for another maths lesson.

It's been great to have you.

Do join me again soon.

Bye-bye!.